Question: Simplify the following expression: $p = \dfrac{-2t^2 - 16t + 18}{t - 1} $
Explanation: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $-2$ , so we can rewrite the expression: $ p =\dfrac{-2(t^2 + 8t - 9)}{t - 1} $ Then we factor the remaining polynomial: $t^2 + {8}t {-9} $ ${-1} + {9} = {8}$ ${-1} \times {9} = {-9}$ $ (t {-1}) (t + {9}) $ This gives us a factored expression: $\dfrac{-2(t {-1}) (t + {9})}{t - 1}$ We can divide the numerator and denominator by $(t + 1)$ on condition that $t \neq 1$ Therefore $p = -2(t + 9); t \neq 1$